On the stability of some systems of exponential difference equations
In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2018-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol38/1/art/opuscula_math_3806.pdf |
| _version_ | 1811202742675308544 |
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| author | N. Psarros G. Papaschinopoulos C. J. Schinas |
| author_facet | N. Psarros G. Papaschinopoulos C. J. Schinas |
| author_sort | N. Psarros |
| collection | DOAJ |
| description | In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations. |
| first_indexed | 2024-04-12T02:44:52Z |
| format | Article |
| id | doaj.art-008878a4e34241ca867204c0dec19d4e |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-04-12T02:44:52Z |
| publishDate | 2018-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-008878a4e34241ca867204c0dec19d4e2022-12-22T03:51:13ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742018-01-0138195115https://doi.org/10.7494/OpMath.2018.38.1.953806On the stability of some systems of exponential difference equationsN. Psarros0G. Papaschinopoulos1C. J. Schinas2Democritus University of Thrace, School of Engineering, Xanthi, 67100, GreeceDemocritus University of Thrace, School of Engineering, Xanthi, 67100, GreeceDemocritus University of Thrace, School of Engineering, Xanthi, 67100, GreeceIn this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.http://www.opuscula.agh.edu.pl/vol38/1/art/opuscula_math_3806.pdfdifference equationsasymptotic behaviourglobal stabilitycentre manifoldbiological dynamics |
| spellingShingle | N. Psarros G. Papaschinopoulos C. J. Schinas On the stability of some systems of exponential difference equations Opuscula Mathematica difference equations asymptotic behaviour global stability centre manifold biological dynamics |
| title | On the stability of some systems of exponential difference equations |
| title_full | On the stability of some systems of exponential difference equations |
| title_fullStr | On the stability of some systems of exponential difference equations |
| title_full_unstemmed | On the stability of some systems of exponential difference equations |
| title_short | On the stability of some systems of exponential difference equations |
| title_sort | on the stability of some systems of exponential difference equations |
| topic | difference equations asymptotic behaviour global stability centre manifold biological dynamics |
| url | http://www.opuscula.agh.edu.pl/vol38/1/art/opuscula_math_3806.pdf |
| work_keys_str_mv | AT npsarros onthestabilityofsomesystemsofexponentialdifferenceequations AT gpapaschinopoulos onthestabilityofsomesystemsofexponentialdifferenceequations AT cjschinas onthestabilityofsomesystemsofexponentialdifferenceequations |